Weyl Integrable Mechanics Resolves Spin-Statistics Theorem, Addressing the Pauli Exclusion Principle for All Particles

The fundamental connection between a particle’s spin and its statistical behaviour has long puzzled physicists, with the inability of traditional mechanics to fully justify the crucial Pauli Exclusion Principle. Now, Enrico Santamato from the University of Naples and Francesco De Martini from the Accademia Nazionale del Lincei, along with their colleagues, present a resolution to this longstanding problem using a framework called Weyl Integrable Mechanics. Their work introduces the concept of ‘intrinsic helicity’, a previously unconsidered property of elementary particles, which naturally emerges from their theoretical approach and correctly predicts the observed spin-statistics connection in nature. This achievement not only reproduces established results like Dirac’s and Schrödinger’s equations, but also proposes a more complete mechanical theory capable of explaining phenomena such as Heisenberg’s uncertainty relations and nonlocal EPR correlations.

Spin Statistics From Quantum Kinematics

This paper presents a derivation of the Spin-Statistics Theorem without relying on standard quantum field theory. The theorem states that particles with integer spin, known as bosons, obey Bose-Einstein statistics, while particles with half-integer spin, known as fermions, obey Fermi-Dirac statistics. This research proves the theorem using a non-relativistic quantum mechanics framework, based on a novel concept of intrinsic angular momentum and a kinematic constraint. The authors introduce intrinsic angular momentum, denoted as sζ, a constant property of elementary particles distinct from orbital angular momentum.

Conservation of this intrinsic angular momentum plays a crucial role in their derivation, linked to a kinematic constraint stating that the rate of change of a specific angle related to the intrinsic angular momentum must be non-negative. The authors propose World Intrinsic Quantum Mechanics (WIQM), built around sζ and the kinematic constraint, using a single scalar wavefunction to describe both bosons and fermions. Differences in behavior arise from the space-time part of this wavefunction, specifically how it relates to the particle’s spin and intrinsic angular momentum, with the Pauli exclusion principle emerging naturally as a consequence of the wavefunction’s space-time component. This work provides an alternative derivation of the Spin-Statistics Theorem without relying on quantum field theory, proposes WIQM as a potentially more complete theory of quantum mechanics, and offers a unified description of bosons and fermions using a single scalar wavefunction. This work introduces intrinsic angular momentum, a conserved property linked to the rotation of a frame attached to each particle, described using three Euler angles, effectively treating particle spin as a consequence of internal rotation and establishing a connection to nonlocal hidden variables. This intrinsic angular momentum is a constant value unaffected by external forces, unlike spin components described in Standard Quantum Mechanics, which can be modified by external fields.

Researchers validated this approach by constructing a theoretical model within the WIQM framework, successfully reproducing established quantum mechanical processes, including Dirac’s and Schrödinger’s equations, Heisenberg’s uncertainty relations, and nonlocal correlations observed in EPR experiments. The WIQM approach naturally incorporates a single rotational sense around the particle’s axis, emerging as a consequence of fundamental principles. The key breakthrough lies in the introduction of intrinsic helicity, or intrinsic angular momentum, as a fundamental property inherent to all elementary particles. This intrinsic angular momentum, denoted as sζ, represents a conserved quantity defining the particle’s rotation around its proper axis, absent from the Standard Mechanics framework.

Standard Mechanics considers only spin components along laboratory axes, while WIQM establishes sζ as a constant value accompanying each spin component, unaffected by external forces. Measurements confirm that sζ remains constant even as other spin components vary, providing a novel physical quantity with significant dynamical properties. The WIQM framework defines a six-dimensional configuration space, incorporating both spatial location and particle orientation, and utilizes a non-trivial transport law for vectors based on Weyl’s geometry. Calculations demonstrate that the scalar curvature within this space is proportional to Bohm’s quantum potential, naturally incorporating quantum phenomena into the theory. The resulting equations reduce to the single Schrödinger equation, successfully reproducing standard quantum mechanical results. By extending standard mechanics to incorporate particle orientation within a six-dimensional space, WIQM introduces the concept of intrinsic helicity, or giration radius, as a fundamental property of elementary particles. This extension allows for a derivation of the Spin-Statistics Connection, explaining how particle spin dictates observed statistical behavior.